Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Optimal Bounds between f-Divergences and Integral Probability Metrics
Authors: Rohit Agrawal, Thibaut Horel
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we systematically study the relationship between these two families from the perspective of convex duality. Starting from a tight variational representation of the f-divergence, we derive a generalization of the moment-generating function, which we show exactly characterizes the best lower bound of the f-divergence as a function of a given IPM. Using this characterization, we obtain new bounds while also recovering in a unified manner well-known results, such as Hoeffding s lemma, Pinsker s inequality and its extension to subgaussian functions, and the Hammersley Chapman Robbins bound. This characterization also allows us to prove new results on topological properties of the divergence which may be of independent interest. |
| Researcher Affiliation | Academia | Rohit Agrawal EMAIL Harvard John A. Paulson School of Engineering and Applied Sciences Cambridge, MA 02138, USA Thibaut Horel EMAIL Institute for Data, Systems, and Society Massachusetts Institute of Technology Cambridge, MA 02139, USA |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. It is a theoretical paper focusing on mathematical derivations and proofs. |
| Open Source Code | No | The paper does not provide any explicit statement about making source code available, nor does it include links to a code repository. |
| Open Datasets | No | This is a theoretical paper that does not perform experiments on specific datasets. It discusses probability distributions and measures at a conceptual level, and therefore does not provide information about open datasets. |
| Dataset Splits | No | This is a theoretical paper and does not involve empirical experiments requiring dataset splits. Therefore, no dataset split information is provided. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not mention any specific software dependencies or version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup details, hyperparameters, or training configurations. |